I posted this earlier:
Even icons painted in a naturalistic style, with linear perspective, shadows cast by the figures and features in the composition, and modeling which reproduces volume, are, strictly speaking, deficient as objects of veneration. These speak of time, place and space as seen through earthly eyes and parameters. Yet, in heaven, there is no time as we know it; there is no night and day, but the Light that never sets, the eternal Day that never ends, where all that is earthly, mortal and corruptible has been transfigured, transformed and perfected. It is these things, and more, which the icon seeks to portray and express, something which a 3D statue is manifestly incapable of doing.
To which I will add:
Orthodox hymnography, particularly the hymns written to the Holy Trinity (troitsny, triadika) frequently refer to the Holy Trinity as the unwaning Light, Christ as the Radiance of the Father, and similar imagery. Christ was transfigured on Mt Tabor in a blaze of uncreated Light, brighter than the sun, and so bright that the three disciples who witnessed this could bear only a glimpse of it. Yet this display was only a fraction of the fullness of divine glory, as the hymns for the feast say.
Christ Himself also said to His disciples: You are the light of the world. Indeed, the words luminary, enlightener, radiant, and their variations, pepper the hymnography of saints. Saints are partakers of the Divine Light, and it is this Light which an icon portrays, the Light which comes from within, the all-encompassing Light where no shadow can be cast, and which, in an icon, culminates in the halo, usually golden, which surrounds the saint's face. A skilled iconographer can express this inner light by careful application of paint and leaf. Coupled with the flatness of the composition, the abstracted, non-naturalistic portrayal, and the deliberate use of inverse perspective which gives the opposite effect to linear perspective, a well-executed and well-composed icon is indeed capable of portraying and expressing heavenly realities.
By contrast, a statue is, by its nature, solid, opaque, volumetric, and, with its three dimensions, shadows are inevitable. It remains earthbound, of this world, not the next. A statue simply cannot portray the inner radiance of the saint as paint applied with skill to a gessoed board can. Indeed, in most non-Orthodox churches I have visited, the statues there are lit by spotlights or similar external illumination, an act which is surely the complete antithesis of the inner light which an icon easily and effortlessly expresses.